Quadrilateral Properties

Worked example

1. 1

   $\text{2 lines, order 2}$ — The clues: 2 lines of symmetry and rotation order 2. Two rows match: rectangle and rhombus.

2. 2

   $\text{diagonals not equal}$ — The next clue. A rectangle's diagonals are always equal, so it cannot be a rectangle.

3. 3

   $\text{rhombus}$ — Only the rhombus is left. Check: its 2 lines of symmetry are its diagonals, which are not equal. It fits.

Worked example

1. 1

   $64^{\circ }\text{and}64^{\circ }$ — The opposite angle of a rhombus is equal, so it is also 64°.

2. 2

   $180^{\circ }-64^{\circ }=116^{\circ }$ — An angle next to it adds to 180° with it, because the two sit between parallel sides. So it is 116°.

3. 3

   $64^{\circ },116^{\circ },64^{\circ },116^{\circ }$ — The four angles in order round the shape. The last 116° is opposite the first one.

4. 4

   $64+116+64+116=360$ — Check: they add to 360°, as every quadrilateral's angles must.

Worked example

1. 1

   $(2x+25)+(x+5)=180$ — Angles next to each other add to 180°. Write this equation first: it earns a mark even if a later line slips.

2. 2

   $3x+30=180$ — Collect like terms: 2x + x = 3x and 25 + 5 = 30.

3. 3

   $3x=150$ — Take 30 from both sides, so the x term is alone.

4. 4

   $x=50$ — Divide both sides by 3.

5. 5

   $2(50)+25=125^{\circ },50+5=55^{\circ }$ — Put x = 50 back in to get the angles. If they ask for the largest angle, it is 125°.

6. 6

   $125+55=180$ — Check: the two angles add to 180°, so x = 50 is right.

Worked example

1. 1

   $A\to B:4\text{ right},0\text{ up}$ — Count the move along side AB. Write it down, because you will copy it.

2. 2

   $D\to C:4\text{ right},0\text{ up}$ — DC is the side opposite AB. In a parallelogram opposite sides are parallel and equal, so DC makes the same move.

3. 3

   $C\to D:4\text{ left},0\text{ down}$ — You start from C, so go the move backwards.

4. 4

   $D=(6-4,4-0)=(2,4)$ — Take 4 from C's x and nothing from its y. That is the fourth corner.

5. 5

   $A\to D:1\text{ right},3\text{ up}$ — Check with the other pair. B to C is also 1 right, 3 up, so AD and BC match. D is right.

Steps

1. 1

   Draw a straight line down the grid. It will be the kite's line of symmetry.

2. 2

   Mark a top corner and a bottom corner on that line.

3. 3

   Mark two side corners level with each other, the same number of squares left and right of the line, nearer the top than the bottom.

4. 4

   Join the four corners in order round the shape.